count_points() error for generic schemes. (includes patch)

[mmarco]

sage raises an error when trying to count the number of points of a subscheme of an affine scheme.

See, for instance:

sage: F=FiniteField(3)
sage: R.<x,y>=F[]
sage: A=AffineSpace(F,2)
sage: I=R.ideal(x^2-y^2-1)
sage: S=A.subscheme(I)
sage: S.count_points(2)



---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)

/home/mmarco/sage-4.6.2/<ipython console> in <module>()

/usr/lib64/python2.7/site-packages/sage/schemes/generic/scheme.py in count_points(self, n)
    531             F1 = GF(q**i, name='z')
    532             S1 = self.base_extend(F1)
--> 533             a.append(len(S1.rational_points()))
    534         return(a)
    535     

/usr/lib64/python2.7/site-packages/sage/schemes/generic/algebraic_scheme.py in rational_points(self, F, bound)
   1129                 raise TypeError, "Unable to enumerate points over %s."%F
   1130         try:
-> 1131             return X.points()
   1132         except TypeError:
   1133             raise TypeError, "Unable to enumerate points over %s."%F

/usr/lib64/python2.7/site-packages/sage/schemes/generic/homset.py in points(self, B)
    162         except TypeError:
    163             raise TypeError, "Domain of argument must be of the form Spec(S)."
--> 164         if is_RationalField(R) or R == Z:
    165             if not B > 0:
    166                 raise TypeError, "A positive bound B (= %s) must be specified."%B

NameError: global name 'Z' is not defined

Apply:

trac_11526_final.patch

[davideklund]

The patch makes sense, it fixes a bug in the method points() of the class SchemeHomset?_affine_coordinates.

Note: the same typo (Z instead of ZZ) seems to occur in the method points() of the class SchemeHomset?_projective_coordinates_ring, which is not implemented yet.

[davideklund]

In addition to fixing the bug, the patch includes a doctest illustrating this.

[davideklund]

The patch trac_11526_bugfix_with_doctest.patch was made using Sage 4.7.1.

[johanbosman]

Now that you're working on the docstring anyway, it would be good to add INPUT and OUTPUT sections to it, as is the standard convention.

[davideklund]

In addition to earlier changes, the patch includes INPUT and OUTPUT info.

[davideklund]

The patch trac_11526_bugfix_with_docstring.patch was made using Sage 4.7.1.

[fschulze]

The same patch as above together with the fix in the projective case.

[saraedum]

fixes the bug (also for the projective case), docstring with Input and Output.

[saraedum]

Apply trac_11526_final.patch

Tested against sage-4.8.alpha3 and doctests pass.

trac_11526_final.patch is identical to [trac_11526_bugfix_with_docstring.2.patch] except for the commit message which I replaced with something that makes hopefully more sense to somebody who does not know this ticket.

We still don't have a docstring for SchemeHomset?_projective_coordinates_ring.points() but I guess that is acceptable since there wasn't any before and it's not implemented anyway.

I'm unsure if "Reviewers" should only mention the person who clicked "positive review" or everybody who was part of the review process. Anyway, I added some authors and reviewers, I hope nobody minds.

Btw. davideklund, your name is not in the AccountNamesMappedtoRealNames? on the trac wiki start page.

[vbraun]

I fixed this long ago in #11599 which also contains some other important additions IMHO. I think it would be more productive if somebody could review #11599.